## Logic Seminar

Slawomir SoleckiCornell University
Orbit equivalence relations induced by actions of Polish groups, part 2
Tuesday, March 6, 2018 - 2:55pm
Malott 206

We introduce a class of Borel equivalence relations, called Polishable, that lies between the class of orbit equivalence relations of Polish group actions and the class of idealistic equivalence relations of Kechris and Louveau. We show that each Borel orbit equivalence relation of a Polish group action admits an approximation by a canonical transfinite sequence of countable length of such equivalence relations. The proof relies on a lemma, that may be interesting in its own right, on stabilization of increasing transfinite sequences of length $\omega_1$ of completely metrizable topologies.